MUNICIPALITIES CLASSIFICATION BASED ON FUZZY RULES Miroslav Hudec INFOSTAT – Bratislava Mirko Vujošević FON – Beograd Lenka Priehradníková

Classification Purpose: estimating of road maintenance needs in winter The data of municipalities are in the Information system MOŠ/MIS (2891 municialities 803 indicators) The tool for classification – fuzzy inference system and his improvement: neuro-fuzzy system

Fuzzy systems These systems are categorised into two families: Mamdani: Takagi-Sugeno-Kang: Ri (i=1,..,l) denotes the i-th fuzzy rule, xj (j=1,...,n), is the input, yi is the output of the fuzzy rule Ri , Aki - is the k-th fuzzy membership function in i-th rule and Bi denotes the output fuzzy membership functions , aji - are the i-th coefficient of the j-th output and i-th rule

Fuzzy systems The basic elements of the fuzzy systems are: Fuzzification Knowledge base Processing of the rules Defuzzification

Fuzzification - length of roads number of days with snow

Fuzzification total yearly rainfalls (precipitation) needs for winter maintenance

Knowledge base IF – THEN rules 1. If length of roads is Very Small and number of days with snow is Very Small and precipitation is Very Small Then maintenance is Very Small.   2. If length of roads is Medium and number of days with snow is Very Small and precipitation is Small Then maintenance is Small. 3. If length of roads is Medium and number of days with snow is Medium and precipitation is Medium Then maintenance is Medium. 4. If length of roads is Medium and number of days with snow is Very High and precipitation is High Then maintenance is High. 5. If length of roads is Very High Then maintenance is Very High.

Processing of the rules and defuzzification The MatLab software and the Sugeno model of the FIS was used in this paper. Processing of the rules: Aggregation, implication and accumulation. Operator min is used as t-norm. Defuzzification is not part of this model.

Results for some selected municipalities

Geographical interpretation

Discussion of Fuzzy systems The classification results were reasonable and expected for selected region. The results may slightly vary with the definition of the particular parameters of the used fuzzy inference system and with the selected method of defuzzification but not so much as with the choices of parameters of membership functions and set of inference rules. No constraints in number of fuzzy sets, rules and ranked municipalities

Neuro-fuzzy system - ANFIS

Advantages of ANFIS ANFIS can improve the process of determining membership functions. Membership functions obtained in fuzzification process depend on parameters and changing the parameters will change the shape of the membership function and ranking results. Because of sensitivity to expert choices of the membership function parameters, these membership function parameters can be modified using ANFIS.

Constraints of ANFIS Neuro-fuzzy systems need sets for training and checking his parameters. Obtained ANFIS structure has 153 parameters. For well trained ANFIS there are needed more than 300 municipalities in training and checking data sets.

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